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"Known as the founder of integral calculus and mathematical physics". I'm a mathematician, and it's a bit of a stretch to call him the founder of integral calculus; that's usually reserved for Newton and Leibnitz. Archimedes came extremely close, as evidenced by his approximation of pi by looking at inscribed and circumscribed polygons about the circle.

Back then, a C actually meant something. I've taught at Ivies and State schools for the past several years. In many of the schools (I'll let you guess which ones), I and my friends have been given 'suggested' grade distributions. I have friends who've been told no matter what, everyone passes b/c the paperwork to fail or give a D is just too much hassle for their professor.

Eek...makes me dizzy. My local school has ranking from the first freshman semester on. Total grade points averaged is the only standard, but AP classes get a few extra points. I guess I'd better be glad for a straightforward system! The one you describe sounds ripe for corruption.

the real problem is that there will often be several people who are approx the same, and it's very tough to distinguish. it's not so bad in HS, but in college how do you compare the different majors? But give us some credit and be honest about it. we become so concerned with making sure everyone feels good about themselves automatically that you can't feel good about what you accomplish. you have to be mature enough to get such feelings from yourself and not others, but that's hard when your young. It really bothers me when we have pushes to put everyone in the same class so the good kids will help the slower kids learn and everyone will be happy. You too often bore the good kids. I don't hear high school sports teams doing this. I was a so-so tennis player, but my school one states several times. No chance of making the team (in two decades of playing against one of my friends, who was one of the worst to make it, I've won one set, probably b/c each set meant a lot more to me than him). This is acceptable, but in academics....

There's often other agendas. I went to a good public school near Boston. We could somehow handle knowing we weren't on the football team, but academics were different. They wouldn't tell us class rank till senior year. They said there was an exact tie b/w myself and someone else (false, I know I was epsilon greater) and they would re-calculate grades after first semester to determine who is Valedictorian. I take 6 APs, all A+s, As and one A-. He takes 5 classes (APs, honors AND college prep classes). Needless to say, it was not even close to a tie anymore, but we both were Valedictorians. Eventually a teacher privately told me what happened: the school LIKES having multiple winners. That way more people can feel good about themselves. They had always meant for there to be two; they had two the previous year and liked it, they had two the following year. Now, the purpose is to get an education, not to be called Valedictorian (I almost didn't take Spanish as I'm not good at languages, but then quickly realized that getting V- at the cost of furthering my education just doesn't feel right). What bothers me is they should say this. Of course, New England has soccer leagues where we don't keep score, so I shouldn't be surprised!

In addition to being historic, what the NYTimes (deliberately) fails to mention is that when the GOP obstructed Clinton's nominees, there were NOT 51 votes to confirm. While as a general principle everyone should get an up or down vote (make the Senators go on record against a nominee), it was a completely different situation. HERE we have a majority of Senators saying they'll support.

Democrats also argue that Republicans are trying to radically change a system that Democrats used sparingly, blocking only 10 of Bush's judicial nominees while confirming more than 200 of them. They say Republicans blocked more Clinton administration nominees by not giving them hearings or votes in the Judiciary Committee.

It's more than that. The Clinton people blocked didn't have the votes to be confirmed; W's did. You can argue that everyone nominated should get an up or down vote, but it's different when 51 people are on record saying they'll confirm as opposed to 51 on record saying they'll vote against.

As a professional mathematician who knows all of the mathematicians mentioned but two (the author and one other), I feel somewhat suited to comment.

I'll leave the statement on "like right-wing policies" for others. For me, I consider the following "a proof". One has a set of definitions, axioms, and assumptions, and the rules of logical implication. For example, if I know that P implies Q (P --> Q) and I know that P is true, the Q must also be true.

I consider something to be proved if by applying the rules of logic it can be deduced from my axioms and assumptions. This leads us to the concept of relative proof, namely, we can show the result follows from our initial assumptions, but we don't know if our initial assumptions are valid.

I'll give two standard examples. Let one of my axioms be that A and not A are both true (A an arbitrary statement). Then it turns out that, using the laws of logic, you can prove ANY statement B is true. Why, it turns out that A and not A both being true is quite powerful. Thus, we have an inconsistent axiom structure, and it isn't surprising that we can deduce anything.

Another example is Russel's Paradox. Mathematicians used to think that given any property P, one can form the set of all x having property P. Russel considered the following: Let R be the collection of all objects x such that x is NOT an element of x. If R is a set, then R is an object having some elements in it. We can ask: is R an element of R? From the definition of R, an object x is in R if and only if x is NOT an element of X. So, if R is not an element of R, then R is in R; if R is an element of R, then R is not in R! Contradiction! Such a set cannot exist, we cannot just collect any group of objects to be a set.

The point to get from this is that there can be lots of surprising subtleties. Things that "look" or "feel" convincing are often false. I would say two major ways for something to be false is that (1) it just doesn't follow from the axioms / assumptions (and you made an argumentative mistake); (2) the original axioms / assumptions are bad / inconsistent, and what you are studying now highlights that.

For the proofs of Fermat and small prime gaps, we weren't finding mistakes with our axioms. We were finding deductive mistakes in very long, very technical, complicated arguments (at least for Fermat, I'm not too familiar with the small gaps paper).

There is a lot more to the subject. It turns out there are many results which can be proven to be undecideable from a set of axioms / assumptions.

But I hope this gives the general idea. He is right that there are different levels of proofs. We have much more "rigorous" proofs than a few centuries ago. We have lots of cases with strong heuristics indicating what "should" be true. The problem is the field is getting very technical. I know -- I write papers in the field, and referee. I've found mistakes by papers from big names where all the arguments are fine, but the lower boundary term of an integral was dropped, and that made all the difference. However, I don't DOUBT that papers like this COULD be successfully refereed, if people took the time. Hales' proof of the Kepler Conjecture (on sphere packing) is a lot harder, as the computer checked numerous cases. So, while some things can be done by hand, the universe may collapse before we finish.

I'm rambling, so I'll stop here. Basically, I look at a "proof" as something that has been shown (step by step by step) to follow from a given set of axioms and assumptions and the rules of logical inference. Just because someone checks every step does NOT mean they checked correctly. Many times we have results that we "accept" as true, without having really done all the details (doing enough so we see the general picture, it looks similar to things we've seen before, so ....). As time is finite, often one reads papers and says "that statement seems plausible", and one keeps reading. If anyone wants to chat more, email sjmiller@math.ohio-state.edu.

I know it somewhat defeats the purpose, but how about an Alphabetical Action bake-sale? Anyone whose name begins with letters A-M pays $1, N - Q pays 50cents, and so on. While it dilutes the point a bit, who can protest something as arbitrary as this? OK, I know very well who could protest.

Or you can do it by their major. English, Politics, Psych pay $1, .... Of course, unlike the Alphabetical, you can still enrage people by saying Women's Studies, African-American Studies pay less.

attention: Leslie Moonves, CEO, CBS-TV
re: upcoming movie on Reagan

On can argue the merits of choosing an actor to star in a movie about a major politician: can actors rise above their political views and give a fair performance of someone they disagree with? I can see both sides to this.

However, I have a harder time seeing both sides of DELIBERATELY including emotionally charged scenes, painting Reagan in a terrible light, which are known to have never happened! I am referring to the scene where Reagan says AIDS victims can all die, as it's their fault; an incident the writer admits there is no substantiating evidence.

We can't show Arabs dancing in the streets when Americans die, but we can make up stories to ruin the reputation of one of our greatest presidents?

If you are not the appropriate person to contact, I apologize. I can only assume that you (or whoever is ultimately responsible) are unaware of this, but now that you know, you will make sure the record is righted.

If you cannot refilm the scene and must go ahead and air it, I suggest the following: IMMEDIATELY after the lines are said, pause the film, and have an announcer state that the following incident has no evidentiary support, but we were unable to re-film the scene; we do not wish to mis-inform the American people.

Sincerely Dr. Steven J. Miller

http://www.thankyoutony.com/

I love the last sentence: Abbas, a former peace negotiator, has met several times in the past with Sharon and has criticized the Palestinians' use of violence in their revolt for statehood. I'd rather end with a sentence from yonif, posted a few days ago:

Abbas, among other terrorist links, was the treasurer of the PLO terrorist group in 1972, the group which massacred the Israeli atheletes in Munich, Germany. He also is a holocaust denier, saying less then 1 million Jews were murdered, and the Zionists had a pact with Hitler to do so. posted on 04/30/2003 12:02 PM PDT by yonif

Why do they say "support / no support" for the first three, and then "it was a bad idea" for the last? For consistency, shouldn't the first choice be "it was a good idea before, and it still is"?

Saturday, February 01, 2003

CAPE CANAVERAL, Fla. — NASA lost communication with space shuttle Columbia as the ship soared over Texas several minutes before landing Saturday morning. It wasn't immediately clear if there was a problem with the shuttle

French President Jacques Chirac vowed, "For us, war is always the proof of failure and the worst of solutions,

I think we're misreading this. He's saying that, for France, war is always proof of failure. This is true. How many hundreds of years do you have to go back before France won a war? It shows how poor their armed forces are, et cetera. It's also, for France, the worst of all solutions because they lose.

Get out of the way, and if you want to leave NATO again, don't let the door hit you on the way out.

How quaint!

Great picture post. I'm in a much better mood to finish my grading....

Sharpton, who has unsuccessfully run for New York mayor and the U.S. Senate, has been outspoken on many local and national issues, most notably on police brutality in the highly publicized cases of Amadou Diallo and Abner Louima in New York, and on the U.S. military bombing on the tiny Puerto Rican island of Vieques. AP 1-21-03

how about some other things he's been outspoken about, such as:

1987: Sharpton spreads the incendiary Tawana Brawley hoax, insisting heatedly that a 15-year-old black girl was abducted, raped, and smeared with feces by a group of white men. He singles out Steve Pagones, a young prosecutor. Pagones is wholly innocent - the crime never occurred - but Sharpton taunts him: ''If we're lying, sue us, so we can ... prove you did it.'' Pagones does sue and eventually wins a $345,000 verdict for defamation. To this day, Sharpton refuses to recant his unspeakable slander (''Never, ever!'') or to apologize for his role in the odious affair. Boston Globe Online - Jan 16, 2003 - Jeff Jacoby

Library Homepage.

I'll be teaching at OSU starting this summer. After years of watching Ivy football, it'll be nice to see real games.

My first year in grad school at Princeton it was Princeton vs Dartmouth. I went wi' a friend who did his undergrad at Florida State. I tried to warn him what Ivy football was like, but he wouldn't believe me, insisting 'football is football.'

Opening play: Dartmouth kicks, it goes through the Princeton receivers legs....

Actually, I won a battle against the Princeton football coach. I was teaching summer calculus, and my students were late because of a football practice. It didn't bother me, as I gave my class a pop quiz, and said there would be a pop quiz ANY day someone showed up late, and late arrivers do not get extra time.

My football players were never late again!

The petition asks the court to order the secretary of state to stop sending out absentee ballots until a replacement for Wellstone is named.

And just when are the Democrats going to name a replacement? Sorry, guys. You've had more than enough time to name a replacement. Why the long delay? Just because you want to milk the event for all it's worth doesn't mean we stop sending out absentee ballots. You want to wait till after the funeral to say who the party nominee will be, that's fine, but there are consequences.

I read (I wish I could remember the source) that a lot of union contracts are $X above minimum wage.